Question: Solve for $x$ and $y$ using elimination. ${-x+4y = 9}$ ${x-5y = -13}$
Explanation: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the equations together. Notice that the terms $-x$ and $x$ cancel out. $-y = -4$ $\dfrac{-y}{{-1}} = \dfrac{-4}{{-1}}$ ${y = 4}$ Now that you know ${y = 4}$ , plug it back into $\thinspace {-x+4y = 9}\thinspace$ to find $x$ ${-x + 4}{(4)}{= 9}$ $-x+16 = 9$ $-x+16{-16} = 9{-16}$ $-x = -7$ $\dfrac{-x}{{-1}} = \dfrac{-7}{{-1}}$ ${x = 7}$ You can also plug ${y = 4}$ into $\thinspace {x-5y = -13}\thinspace$ and get the same answer for $x$ : ${x - 5}{(4)}{= -13}$ ${x = 7}$